ENGLISH ABSTRACT: We propose a new methodology, based on proper scoring rules, for the evaluation
of the goodness of pattern recognizers with probabilistic outputs. The
recognizers of interest take an input, known to belong to one of a discrete set
of classes, and output a calibrated likelihood for each class. This is a generalization
of the traditional use of proper scoring rules to evaluate the goodness
of probability distributions. A recognizer with outputs in well-calibrated probability
distribution form can be applied to make cost-effective Bayes decisions
over a range of applications, having di fferent cost functions. A recognizer
with likelihood output can additionally be employed for a wide range of prior
distributions for the to-be-recognized classes.
We use automatic speaker recognition and automatic spoken language
recognition as prototypes of this type of pattern recognizer. The traditional
evaluation methods in these fields, as represented by the series of NIST Speaker
and Language Recognition Evaluations, evaluate hard decisions made by the
recognizers. This makes these recognizers cost-and-prior-dependent. The proposed
methodology generalizes that of the NIST evaluations, allowing for the
evaluation of recognizers which are intended to be usefully applied over a wide
range of applications, having variable priors and costs.
The proposal includes a family of evaluation criteria, where each member
of the family is formed by a proper scoring rule. We emphasize two members
of this family: (i) A non-strict scoring rule, directly representing error-rate
at a given prior. (ii) The strict logarithmic scoring rule which represents
information content, or which equivalently represents summarized error-rate,
or expected cost, over a wide range of applications.
We further show how to form a family of secondary evaluation criteria,
which by contrasting with the primary criteria, form an analysis of the goodness
of calibration of the recognizers likelihoods.
Finally, we show how to use the logarithmic scoring rule as an objective
function for the discriminative training of fusion and calibration of speaker
and language recognizers.